The bad news is that industry-wide, the average "fall-off" rate is 10 percent. That means 1 out of 10 assignments fails to start or finish on the contracted date. That is actually my real life average as well over the course of 17 years of travel. The good news is that you can greatly reduce those odds, either preemptively or when on an assignment. Some have traveled longer than me without a single major issue. You can also reduce the financial consequences when it does happen.
Traveling can be unpredictable, as is real life. You should always maintain a financial cushion for life's unexpected events. Could be a physical injury or personal illness, a family event, or an unexpected low census at a hospital leading to termination.
Improving your odds are simple common sense and research. Don't oversell your abilities, don't take known bad assignments or work with known bad player agencies, understand there are often good reasons why an assignment is paying more than similar assignments, research the hospitals and agencies on traveler forums and simple news (I don't go to hospitals under bankruptcy protection for example - risk of not being paid is too high). Once on the job, projecting professionalism and confidence is the key. No complaining, no gossiping, positive attitude, and going out of your way to help others. Do things their way, even when it is dumb. Don't think you will be treated like staff, no get out of jail free card for whiny travelers. Let staff do their thing, it is your job to be professional. It is only three months, think survival.
Your odds will go up to at least 1 in 20 if not more (that is like 5 yrs of assignments). That is completely doable. Even though my ratio is industry average, I have profited tremendously by being a traveler. I have benefited professionally, and financially much more than I could have as staff.